Warm Up Find the unit rate. 1. 18 miles in 3 hours 2. 6 apples for $3.30 3. 3 cans for $0.87 4. 5 CD’s for $43

ANSWERS Warm Up Find the unit rate. 1. 18 miles in 3 hours 2. 6 apples for $3.30 3. 3 cans for $0.87 4. 5 CD’s for $43 ANSWERS 6 mi/h $0.55 per apple $0.29 per can $8.60 per CD

Learn to find equivalent ratios and identify proportions. I will… Learn to find equivalent ratios and identify proportions.

Vocabulary equivalent ratios proportion

THINK & DISCUSS the next two slides

Students in Mr. Howell’s math class are measuring the width w and the length l of their faces. The ratio of l to w is 6 inches to 4 inches for Jean and 21 centimeters to 14 centimeters for Pat.

Equivalent ratios are ratios that name the same comparison. These ratios can be written as the fractions and . Since both simplify to , they are equivalent. Equivalent ratios are ratios that name the same comparison. 6 4 21 14 3 2

Take more NOTES

An equation stating that two ratios are equivalent is called a proportion. The equation, or proportion, below states that the ratios and are equivalent. 6 4 21 14 6 4 21 14 =

You can read the proportion Reading Math You can read the proportion by saying “six is to four as twenty-one is to fourteen.” 6 4 = 21 14

If two ratios are equivalent, they are said to be proportional to each other, or in proportion.

Example 1a: Comparing Ratios in Simplest Forms Determine whether the ratios are proportional. 24 51 , 72 128 Simplify . 24 51 24 ÷ 3 51 ÷ 3 = 8 17 Simplify . 72 128 72 ÷ 8 128 ÷ 8 = 9 16 8 17 Since = , the ratios are not proportional. 9 16

Example 1b , 150 105 90 63 Simplify . 150 105 150 ÷ 15 105 ÷ 15 = 10 7 90 ÷ 9 63 ÷ 9 = 10 7 Simplify . 90 63 10 7 Since = , the ratios are proportional.

I try! – Practice on the BOARD! Determine whether the ratios are proportional. 54 63 , 72 144 Click for answers! 135 75 , 9 4

Determine whether the ratios are proportional. I try! – ANSWERS!! Determine whether the ratios are proportional. 54 63 , 72 144 6 7 Since = , the ratios are not proportional. 1 2 135 75 , 9 4 9 5 Since = , the ratios are not proportional. 4

(see the next slide for steps) For the next problem… Write the chart ONLY …then… Work out the problem (see the next slide for steps)

Example 2: Comparing Ratios Using a Common Denominator Directions for making 12 servings of rice call for 3 cups of rice and 6 cups of water. For 40 servings, the directions call for 10 cups of rice and 19 cups of water. Determine whether the ratios of rice to water are proportional for both servings of rice. 19 10 40 6 3 12 Cups of Water Cups of Rice Servings of Rice

Working it Out! Ratio of rice to water, 12 servings: Directions for making 12 servings of rice call for 3 cups of rice and 6 cups of water. For 40 servings, the directions call for 10 cups of rice and 19 cups of water. Determine whether the ratios of rice to water are proportional for both servings of rice. Write the ratios of rice to water for 12 servings and for 40 servings. 3 6 Ratio of rice to water, 12 servings: Write the ratio as a fraction. 10 19 Ratio of rice to water, 40 servings: Write the ratio as a fraction Write the ratios with a common denominator, such as 114. 3 6 3 · 19 6 · 19 57 114 10 19 10 · 6 19 · 6 60 114 = = = = 57 114 60 114 Since = , the two ratios are not proportional.

I try! – Practice on the BOARD! Use the data in the table to determine whether the ratios of beans to water are proportional for both servings of beans. 9 13 35 3 4 8 Cups of Water Cups of Beans Servings of Beans Click for answer.

I try! – ANSWER Use the data in the table to determine whether the ratios of beans to water are proportional for both servings of beans. 9 13 35 3 4 8 Cups of Water Cups of Beans Servings of Beans 36 27 39 27 Since = , the two ratios are not proportional.

You can find an equivalent ratio by multiplying or dividing both terms of a ratio by the same number.

Example 3: Finding Equivalent Ratios and Writing Proportions Find a ratio equivalent to each ratio. Then use the ratios to find a proportion. Possible Answers: 3 5 A. 3 5 3 · 2 5 · 2 6 10 = = Multiply both the numerator and denominator by any number such as 2. 3 5 6 10 = Write a proportion. B. 28 16 28 16 28 ÷ 4 16 ÷ 4 Divide both the numerator and denominator by any number such as 4. 7 4 = = 28 16 7 4 = Write a proportion.

I try! – Practice on the BOARD! Find at least THREE ratios equivalent to each ratio. Then use the ratios to write proportions. 3a: 3b: 3c: 2 3 16 12 38 18

Lesson Quiz

Determine whether the ratios are proportional. 9 30 12 40 12 21 10 15 1. 2. , , Find a ratio equivalent to each ratio. Then use the ratios to write a proportion. 3 8 3 7 3. 4. 5. In preschool, there are 5 children for every one teacher. In another preschool there are 20 children for every 4 teachers. Determine whether the ratios of children to teachers are proportional in both preschools.